Learning Objectives:

__Math Tutoring on Graphing Rational Functions__

**Functions **are** **given by the quotient, or ratio, of two polynomials, are called **rational functions.** Notice there is a numerator and denominator, and both the numerator and denominator are polynomial functions. The domain of a **rational function** is restrictive to those **x **values that do not result in division by zero. Remember, we are not allowed to have zero in the denominator of a fraction. To determine the domain of a **rational function**, we will set the denominator equal to zero and solve. The **graphs of rational functions **can be rather complicated to a **graph**. First, we find the intercepts if there are any. Then we find the **vertical asymptotes** by setting the denominator equal to zero and solving. However, the **graphs of rational functions **often have **holes**. Let’s review where those **holes** will occur at a zero of the denominator that is also a zero of the numerator. We should look for common factors between the numerator and denominator in factored form. A **vertical asymptote** will occur at the zero of the denominator that is not a zero of the numerator. We also find the** horizontal asymptote**, if it exists, using the fact above. Finally, sketch the **graph**.

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**Hook Questions:**

*1. **How do you find holes in a rational function?*

*2. **What is the definition of a rational function?*

*3. **How do you find Asymptotes?*

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